Should the words double dutch be capitalized in sentence The Plainville girl scouts held a jump rope show?

No, "double dutch" should not be capitalized in the sentence "The Plainville Girl Scouts held a jump rope show."

Here's why:

* Double Dutch is a specific type of jump rope activity, not a proper noun. Proper nouns are names of specific people, places, or things (e.g., John, London, Eiffel Tower).

* Jump rope is a general term for the activity, not a specific name.

Therefore, the sentence should read: "The Plainville Girl Scouts held a jump rope show."